Data & Probability · Working with data · 2.3

Compare data sets.

To compare two data sets, compute a summary for each — often the mean — and compare. The set with the larger mean has higher values on average, even if individual values overlap.

01 / THE IDEA

See it work.

Watch the method

Compare data sets

Find each set’s mean, then compare.

1 / 2
Find the compare-mean of: .
1

Add the values

Find the total of every value in the set.

NaN=NaNNaN = NaN
2

Divide by how many

The mean is the total divided by the number of values.

NaN1=NaN\frac{NaN}{1} = NaN
— / WHY IT WORKS

The idea underneath.

Summary vs summary

Comparing whole data sets is easiest through one number each, like the mean.

Why it works

Reduce each to its average, then judge.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Set A: 6, 3, 8, 6. Set B: 9, 2, 9, 8. Which has the higher mean?

1

Answer

Set B

EX 2medium

Set A: 2, 8, 3, 10. Set B: 2, 2, 3, 3. Which has the higher mean?

1

Answer

Set A

EX 3hard

Set A: 10, 2, 9, 4. Set B: 8, 8, 2, 3. Which has the higher mean?

1

Answer

Set A

04 / COMMON TRAPS

Where students slip.

Trap

Comparing single values.

Fix

Compare the summaries (means), not one number each.

Trap

Forgetting to divide.

Fix

Use the mean, not just the sum, if the counts differ.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Set A: 2, 8, 3, 3. Set B: 4, 6, 5, 6. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
C2

Set A: 10, 8, 5, 6. Set B: 3, 10, 10, 4. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
C3

Set A: 5, 3, 3, 9. Set B: 3, 9, 6, 5. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
C4

Set A: 3, 8, 3, 7. Set B: 5, 10, 10, 8. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
Apply

Apply (4)

A1

Set A: 7, 2, 2, 7. Set B: 3, 6, 2, 6. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
A2

Set A: 7, 8, 9, 7. Set B: 5, 4, 5, 9. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
A3

Set A: 5, 2, 8, 6. Set B: 6, 2, 10, 6. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
A4

Set A: 3, 2, 8, 9. Set B: 6, 3, 10, 4. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
Extension

Extension (4)

E1

Set A: 6, 2, 3, 5. Set B: 6, 7, 4, 4. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
E2

Set A: 3, 7, 2, 9. Set B: 3, 9, 8, 10. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
E3

Set A: 7, 4, 8, 8. Set B: 8, 7, 2, 5. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.
E4

Set A: 7, 2, 7, 3. Set B: 5, 9, 2, 3. Which has the higher mean?

Need a hint?
  • Find the mean of each set.
  • Compare the two means.